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Notification Bot (Nov 09 2021 at 18:36):Stream created by John Baez.
John Baez (Nov 09 2021 at 18:38):This is a thread for discussing the use of categories, operads and the like in thermodynamics. I expect that most of the time it'll be just me and @Owen Lynch talking about these topics: he's doing his master's thesis at the University of Utrecht on 'compositional thermodynamics'.
John Baez (Nov 09 2021 at 18:45):Next time we meet, I hope:
@Owen Lynch can explain some of Caratheodory's work to me. Hey, Owen, can you point me to that long paper of his again? I'm not finding it.
I can explain some of Simon Willerton's ideas on the Legendre-Fenchel transform. Notice that he uses categories enriched over ! This is a good sign that our first paper was on the right track.
Owen Lynch (Nov 09 2021 at 18:55):Here's the Caratheodory paper: http://neo-classical-physics.info/uploads/3/0/6/5/3065888/caratheodory_-_thermodynamics.pdf
John Baez (Nov 09 2021 at 19:02):Thanks!
Jules Hedges (Nov 10 2021 at 15:55):John Baez said:
This is a thread for discussing the use of categories, operads and the like in thermodynamics. I expect that most of the time it'll be just me and Owen Lynch talking about these topics: he's doing his master's thesis at the University of Utrecht on 'compositional thermodynamics'.
In my opinion this is a strong candidate to be a topic in the #practice: applied ct stream, and not a stream in its own right. (I've unfollowed virtually all "single topic" streams that people have created over time)
Morgan Rogers (he/him) (Nov 10 2021 at 16:01):The stated expected use would lead me to agree, but perhaps thermodynamics is a broader subject than I appreciate so that there are lots of potential topics here.
John Baez (Nov 10 2021 at 18:01):I imagine we're going to want to spawn a lot of sub-topics here, so we can keep straight all the topics Owen I discuss for his thesis in the next year. Also I may start a Zoom discussion series with the biochemist Hong Qian. It would be great if topics could have sub-topics, but they can't.
John Baez (Nov 10 2021 at 18:02):I promise to write large numbers of comments here in the next year, on many topics. Jules can unfollow this stream.
John Baez (Nov 11 2021 at 02:24):By the way: anyone who wants to comment on this stream should feel free to!
That should go without saying. But one reason Owen and I are talking here rather than privately is so other people can join in and maybe help out now and then.
Henry Story (Nov 11 2021 at 13:06):As a philosophical interest, I'd love to be able to listen to a lecture at some point, when the concepts are settled a bit, that would explain the relation between entropy and negentropy in categorical terms.
Kale Evans (Dec 17 2021 at 04:39):Does anyone have any experience or know of any applications applying category theory to fluid dynamics? I'm recently looking into some problems involved in this field, and was wondering if there are any categorical perspectives on it
Owen Lynch (Dec 29 2021 at 19:25):yes! @James Fairbanks and @Evan Patterson are using Catlab to do computational fluid dynamics.
Owen Lynch (Dec 29 2021 at 19:25):@Evan Patterson is working on a categorification of the discrete exterior calculus for this effort.
John Baez (Dec 29 2021 at 20:14):Owen is using "categorification" to mean "applying categories to something", not "replacing set-theoretic concepts by their category-theoretic analogues". I try to force people to use it the latter way.
Evan Patterson (Dec 30 2021 at 00:49):Thanks for the mention, Owen. My collaborators and I have indeed been working on categorical approaches to computational physics, with fluid dynamics being one of the main examples. I said a bit about this work in the second half of a talk I gave earlier this month, but unfortunately that's all we have out there so far. One of my main priorities early next year will be writing some papers about this work.
Slides and video for my talk this week at the @ToposInstitute colloquium: https://www.algebraicjulia.org/assets/slides/topos-colloquium-2021.pdf https://www.youtube.com/watch?v=Ra-PLnog_M0 The talk had two mostly unrelated parts.
- Evan Patterson (@ejpatters)